Next-to-Maximal Helicity Violating Amplitudes in Gauge Theory

Using the novel diagrammatic rules recently proposed by Cachazo, Svrcek, and Witten, I give a compact, manifestly Lorentz-invariant form for tree-level gauge-theory amplitudes with three opposite helicities.Comment: 12 pages, 1 figur

Two-Loop ϕ4\phi^4-Diagrams from String Theory

Using the {\em cutting and sewing} procedure we show how to get Feynman diagrams, up to two-loop order, of $\Phi^{4}$-theory with an internal SU(N) symmetry group, starting from tachyon amplitudes of the open bosonic string theory. In a properly defined field theory limit, we easily identify the corners of the string moduli space reproducing the correctly normalized field theory amplitudes expressed in the Schwinger parametrization.Comment: 28 pages, 12 figure

Relations between some analytic representations of one-loop scalar integrals

We compare several parametrized analytic expressions for an arbitrary off-shell one-loop $n$-point function in scalar field theory in $D$-dimensional space-time, and show their equivalence both directly and through path-integral methods.Comment: 12 pages, NIKHEF-H/94-2

Dual conformal constraints and infrared equations from global residue theorems in N=4 SYM theory

Infrared equations and dual conformal constraints arise as consistency conditions on loop amplitudes in N=4 super Yang-Mills theory. These conditions are linear relations between leading singularities, which can be computed in the Grassmannian formulation of N=4 super Yang-Mills theory proposed recently. Examples for infrared equations have been shown to be implied by global residue theorems in the Grassmannian picture. Both dual conformal constraints and infrared equations are mapped explicitly to global residue theorems for one-loop next-to-maximally-helicity-violating amplitudes. In addition, the identity relating the BCFW and its parity-conjugated form of tree-level amplitudes, is shown to emerge from a particular combination of global residue theorems.Comment: 21 page

On the Coupling of Gravitons to Matter

Using relationships between open and closed strings, we present a construction of tree-level scattering amplitudes for gravitons minimally coupled to matter in terms of gauge theory partial amplitudes. In particular, we present examples of amplitudes with gravitons coupled to vectors or to a single fermion pair. We also present two examples with massive graviton exchange, as would arise in the presence of large compact dimensions. The gauge charges are represented by flavors of dynamical scalars or fermions. This also leads to an unconventional decomposition of color and kinematics in gauge theories.Comment: RevTex, 4 page

Monodromy--like Relations for Finite Loop Amplitudes

We investigate the existence of relations for finite one-loop amplitudes in Yang-Mills theory. Using a diagrammatic formalism and a remarkable connection between tree and loop level, we deduce sequences of amplitude relations for any number of external legs.Comment: 24 pages, 6 figures, v2 typos corrected, reference adde

The Structure of Multiloop Amplitudes in Gauge and Gravity Theories

We review the recently discovered duality between color and kinematics in gauge theories. This duality leads to a remarkably simple double-copy relation between diagrammatic numerators of gravity scattering amplitudes and gauge-theory ones. We summarize nontrivial evidence that the duality and double-copy property holds to all loop orders. We also comment on other developments, including a proof that the gauge-theory duality leads to the gravity double-copy property, and the identification of gauge-theory Lagrangians whose double copies yield gravity Lagrangians.Comment: To appear in Proceedings of Loops and Legs in Quantum Field Theory, Woerlitz, Germany, April 25-30, 2010; 4 figure

Multiple Singular Emission in Gauge Theories

I derive a class of functions unifying all singular limits for the emission of a given number of soft or collinear gluons in tree-level gauge-theory amplitudes. Each function is a generalization of the single-emission antenna function of ref. [1]. The helicity-summed squares of these functions are thus also generalizations to multiple singular emission of the Catani--Seymour dipole factorization function.Comment: Corrections for final journal version (sign in eqn. (6.11), equation references, typos in indices) & removal of comment about FD

Loops in Twistor Space

We elucidate the one-loop twistor-space structure corresponding to momentum-space MHV diagrams. We also discuss the infrared divergences, and argue that only a limited set of MHV diagrams contain them. We show how to introduce a twistor-space regulator corresponding to dimensional regularization for the infrared-divergent diagrams. We also evaluate explicitly the `holomorphic anomaly' pointed out by Cachazo, Svrcek, and Witten, and use the result to define modified differential operators which can be used to probe the twistor-space structure of one-loop amplitudes.Comment: 21 pages, TeX. v3. missing citations added. v4. subtlety with the i \epsilon prescription clarifie